You have a friend who likes to try and classify the cars that drive past their bedroom window, but you think that you can build a convolutional neural network that can do a better job than your friend. To test how well your CNN works you test it on 140 cars. Let Z; be equal to 1 if the ith car make and model is correctly classified and 0 otherwise, for i = 1,...,140. (a) What is the statistic that you will use to estimate the accuracy of your CNN? How do you compute it using Z, Z2, ..., Z140? (b) Assuming that the accuracy of your algorithm is 0.94, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal distribution. (Round your standard deviation to 3 sig figs.) (c) Your friend correctly classifies 97% of cars that they see on average. What is the probability that your randomly drawn sample is such that your sample statistic from (a) is higher than 0.97? (Round to 3 sig figs.) (d) You CNN's performance would be indistinguishable from your friend's performance if the sample of 140 cars allows you to construct a symmetric 95% confidence interval that contains 0.97. Say your algorithm correctly classifies 126 cars. Is your CNN's performance indistinguishable from your friend's performance?